In [1]:
#Implement the function given below and plot its two cycles. Plot its histogram also. f(t) = cost*cos5t + cos5t
import matplotlib.pyplot as plt
import numpy as np 
x = np.linspace(0,2*np.pi, 1000)
y = np.cos(x)*np.cos(5*x) + np.cos(5*x)
plt.plot(x,y)
plt.show()
In [2]:
"""Implement the functions given below and plot two cycles of them. Plot scatter plot to
study their relationship.
f1(t) = sint
f2(t) = cost"""

import matplotlib.pyplot as plt
import numpy as np 
x = np.linspace(0,2*np.pi, 1000)
y1= np.sin(x)
y2= np.cos(x)
plt.scatter(x,y1)
plt.scatter(x,y2)
plt.show()
In [3]:
"""Generate and plot the waveform given below and plot its histogram also. half wave recitifier"""
import matplotlib.pyplot as plt
import numpy as np 
x = np.linspace(0,4,1000)
y = []
for i in x:
    if np.sin(np.pi*i)>0:
        y.append(np.sin(np.pi*i))
    else:
        y.append(0)
plt.plot(x,y)
plt.show()
In [4]:
"""Read the given csv file: ‘waveform2.csv’ as an array and plot it. Plot its histogram with an
appropriate bin size."""
import matplotlib.pyplot as plt #there was no download link so i just took the above problem and to depict saving in .csv file and reading from it
import numpy as np  #I used the above problem
x = np.linspace(0,4,1000)
y = []
for i in x:
    if np.sin(np.pi*i)>0:
        y.append(np.sin(np.pi*i))
    else:
        y.append(0)
np.savetxt('waveform2.csv',[x,y], delimiter=',')
data=np.genfromtxt('waveform2.csv', delimiter=',')
plt.hist(data[1], bins=100)
plt.show()
In [5]:
"""Realize the function y=2+5sin(2πft) for f=1KHz and plot it. Write values of the function as a
csv file such that the sampling time should be the first value followed by its samples."""
import matplotlib.pyplot as plt
import numpy as np 
import time
xmin=0
xmax=1
ymin=-4
ymax=7
plt.axis([xmin, xmax, ymin, ymax])
tic = time.process_time()
x = np.linspace(0,2*np.pi, 1000)
f = 1000 #Hz
y = 2 + 5*np.sin(2*np.pi*f*x)
plt.plot(x,y)
plt.show()
data=[f]
for i in y:
    data.append(i)
toc = time.process_time()
data.insert(0,(toc-tic)*1000)
np.savetxt("functionSample.csv", data,delimiter=',')
print("Sampling time: ",(toc-tic)*1000) #time difference in milli seconds

Sampling time:  0.0
In [6]:
"""Write and execute a function to solve for the current transient through an RL network (with 
R/L = 1) that is driven by the signal 5e^–t U(t). Plot the current through the circuit.
"""
"""
V(t) = RI + LdI/dt
dI/dt = V(t) -RI/L
"""
from scipy.integrate import odeint
import matplotlib.pyplot as plt
import numpy as np

def model(y,t):
    dydt = 5*np.exp(-t) - y
    return dydt
RL = 1
R = 1
V = 5
i0 = V/R
t = np.linspace(0,20)
sol = odeint(model, i0, t)
plt.plot(sol, t)
plt.show()

image.png

In [7]:
import matplotlib.pyplot as plt
import numpy as np 

t = np.linspace(0,100,1000)
V=[]
w = np.pi/10
v = 5
for j in range(1,100):
    v = v + (40/((2*j + 1)*np.pi)**2)*np.cos((2*j + 1)*w*t)
plt.plot(t, v)
plt.show()

image.png

In [8]:
import matplotlib.pyplot as plt
import numpy as np 
from scipy.integrate import odeint

def model(y,t):
    b = 0.05
    m=0.01
    L = 0.5
    g = 9.8
    y,z = y
    dydx = [z,(-b/m)*z + -(g/L)*np.sin(y)]
    return dydx
t = np.linspace(0,5,100)
sol = odeint(model, [0,3], t)
plt.plot(t,sol[:,0])
plt.show()
In [9]:
"""Plot a sinc function from time t = -10 to 10 and plot its histogram also"""
import matplotlib.pyplot as plt
import numpy as np 
t = np.linspace(-10,10,1000)
y = np.sinc(t)
plt.plot(t,y)
plt.show()
plt.hist(y,bins=100)
plt.show()

image.png

In [10]:
import matplotlib.pyplot as plt
import numpy as np 
T = int(input('enter a number'))
t = np.linspace(0,10,100)
y = []
for i in t:
    temp = 0
    for j in range(1,200,2):
        temp = temp + (1/j)*(np.sin((j*np.pi*i)/T))
    temp = temp * (4/np.pi)
    y.append(temp)
plt.plot(t,y)
plt.show()

image.png

In [11]:
import matplotlib.pyplot as plt
import numpy as np 
t = np.linspace(-10,10,100)
y = []
for i in t:
    if i >= -5 and i <= 5:
        y.append(4*(t**2))
    else:
        y.append(100) 
plt.boxplot(y,showmeans=True)
plt.show()

image.png

In [12]:
import matplotlib.pyplot as plt
import numpy as np 
from scipy.integrate import odeint

def model(y,x):
    y,z = y
    dydx = [z,-0.5*z - 7]
    return dydx

i0 = [21,12]

x = np.arange(0,5,0.5)

sol = odeint(model, i0, x)
plt.plot(x,sol[:,0])
plt.show()
plt.stem(x,sol[:,0])
plt.show()
In [13]:
"""Given a series circuit consisting of a series circuit consisting of a device which has an
inductance of 1 H ,resistance of 22 Ώ and a a capacitor of 200µF and an input voltage of 12 V
DC .If the initial charge and current are both zero, write a program to plot the charge and
current at the time t= 0 to 10s."""

"""
L dI2/d2t + R dI/dt + 1/c I = V'
"""
import matplotlib.pyplot as plt
import numpy as np 
from scipy.integrate import odeint

def model(i,t):
    L = 1
    R = 22
    C = 200e-6
    V = 12
    i,z = i
    didt = [z/L,-(R*z) - i/(C)]
    return didt


i0 = [12/22,0]

t = np.linspace(0,10,100)
sol = odeint(model, i0, t)

plt.plot(t, sol[:,0])
plt.show()

image.png

In [14]:
import matplotlib.pyplot as plt
import numpy as np 
from scipy.integrate import odeint

def model(T,t):
    k=-0.55
    Ts = 25
    return k*(T-Ts)
t = np.arange(0,12,1)
t0 = 60
sol = odeint(model, t0, t)
plt.plot(t,sol)
plt.show()
In [15]:
""""7. Implement the function given below and plot its two cycles. Plot its box plot also and
write down the mean and third quartile value.
f(t) = 3+ sin3t+sin5t"""
import matplotlib.pyplot as plt
import numpy as np 
t = np.linspace(0,2*np.pi, 100)
f = []
for i in t:
    f.append(3+np.sin(3*i)+np.sin(5*i))
plt.boxplot(f,showmeans=True)
plt.show()

image.png

In [16]:
import matplotlib.pyplot as plt
import numpy as np 
from scipy.integrate import odeint
"""
half life T = ln 2 /  λ
"""
def model(N,t):
    return -np.log(2)*N/(5)
i0 = 600
t = np.linspace(0,100, 10000) # days
sol = odeint(model, i0, t)
plt.ylabel('Bismuth (mg)')
plt.xlabel('Time (days)')
plt.plot(t,sol[:,0])
plt.show()

image.png

In [17]:
import matplotlib.pyplot as plt
import numpy as np 

f1 = []
f2 = []
x = np.linspace(0,100,100)
L = 20
for i in x: 
    temp = 0
    for j in range(1,20,2):
        temp = temp + ((-1)**((j-1)/2)/(j**2))*np.sin((j*np.pi*i)/L)
    temp = temp * (8/np.pi)
    f1.append(temp)
    temp = 0
    for j in range(1,100,2):
        temp = temp + ((-1)**((j-1)/2)/(j**2))*np.sin((j*np.pi*i)/L)
    temp = temp * (8/np.pi)
    f2.append(temp)
plt.plot(x,f1)
plt.plot(x,f2)
plt.show()

image.png

In [18]:
ap, cp, wp = 26.2, 21, 10.1
ac, cc, wc = 40.2, 44.8, 14.3
af, cf, wf = 71.2, 63.5, 82.8
print("Amount of proteins in mixture 1: ", 26.2*6+21*3+10.1*1)
print("Amount of proteins in mixture 2: ", 26.2*3+21*6+10.1*1)
print("Amount of proteins in mixture 3: ", 26.2*3+21*1+10.1*6)

print("Amount of carbohydates in mixture 1: ",40.2*6+44.8*3+14.3*1)
print("Amount of carbohydates in mixture 2: ",40.2*3+44.8*6+14.3*1)
print("Amount of carbohydates in mixture 3: ",40.2*3+44.8*1+14.3*6)

print("Amount of Fat in mixture 1: ", 71.2*6+63.5*3+82.8*1)
print("Amount of Fat in mixture 1: ", 71.2*3+63.5*6+82.8*1)
print("Amount of Fat in mixture 1: ", 71.2*3+63.5*1+82.8*6)

Amount of proteins in mixture 1:  230.29999999999998
Amount of proteins in mixture 2:  214.7
Amount of proteins in mixture 3:  160.2
Amount of carbohydates in mixture 1:  389.90000000000003
Amount of carbohydates in mixture 2:  403.7
Amount of carbohydates in mixture 3:  251.20000000000002
Amount of Fat in mixture 1:  700.5
Amount of Fat in mixture 1:  677.4
Amount of Fat in mixture 1:  773.9

image.png

In [19]:
import numpy as np 
A = np.array([[1,2,3,4,5],[0,2,3,4,5],[0,0,3,4,5],[0,0,0,4,5],[0,0,0,0,5]])
w, v = np.linalg.eig(A)
print("Eigen Values are", w)
print("A^2: ", A.dot(A))

Eigen Values are [1. 2. 3. 4. 5.]
A^2:  [[ 1  6 18 40 75]
 [ 0  4 15 36 70]
 [ 0  0  9 28 60]
 [ 0  0  0 16 45]
 [ 0  0  0  0 25]]

image.png

In [20]:
import numpy as np 
import matplotlib.pyplot as plt
x = np.arange(1,40,1)
y = []
big = 0
for i in x:
    if i%10==0:
        big = i
    if i>big and i<big+10:
        if big%20==0:
            y.append(5)
        else:
            y.append(0)
    else:
        y.append(0)
plt.plot(x,y)
plt.show()

image.png

In [21]:
import numpy as np 
A = [[2,1,1],[1,3,2],[2,1,2]] 
"""
 each column has the number of hours put in by a particular product in machine of that column number
 or in other words
 each row is the sum of product of time required by the product in that machine and the total number of products 
 amounting to fully utilize the total time of that machine, i.e. the result of the sum
"""
B = [3*60, 5*60, 4*60]
solution = np.linalg.solve(A,B)
print("A Type: ",solution[0])
print("B Type: ",solution[1])
print("C Type: ",solution[2])

A Type:  36.0
B Type:  48.0
C Type:  60.0

image.png

In [22]:
import numpy as np 
from sympy import Symbol

t = Symbol('t')
s = 3*t**4 - 40*t**3 + 126*t**2 -9
v = s.diff(t)
a = s.diff(t,2)
print("Velocity at instant 0: ",v.subs(t,0))
print("Velocity at instant 3: ",v.subs(t,3))
print("Velocity at instant 5: ",v.subs(t,5))
print("Velocity at instant 7: ",v.subs(t,7))
print("Velocity at instant 10: ",v.subs(t,10))

print("Acceleration  at instant 0: ",a.subs(t,0))
print("Acceleration  at instant 3: ",a.subs(t,3))
print("Acceleration  at instant 5: ",a.subs(t,5))
print("Acceleration  at instant 7: ",a.subs(t,7))
print("Acceleration  at instant 10: ",a.subs(t,10))

Velocity at instant 0:  0
Velocity at instant 3:  0
Velocity at instant 5:  -240
Velocity at instant 7:  0
Velocity at instant 10:  2520
Acceleration  at instant 0:  252
Acceleration  at instant 3:  -144
Acceleration  at instant 5:  -48
Acceleration  at instant 7:  336
Acceleration  at instant 10:  1452
In [23]:
"""
After t seconds an object is moving at a speed of  te-t/2 . Write a program to find the distance
travelled by the object at t=0,10 and 100s"""

import numpy as np 
from scipy.integrate import quad
import matplotlib.pyplot as plt
def func(t):
    return t*np.exp(-t/2)
print("Distance travelled at time t = 0s :", quad(func,0,0)[0])
print("Distance travelled at time t = 10s :", quad(func,0,10)[0])
print("Distance travelled at time t = 100s :", quad(func,0,100)[0])
#extras
t = np.linspace(0,100,100)
d = []
v = t*np.exp(-t/2)
for i in t:
    d.append(quad(func,0,i)[0])
plt.plot(t,d)
plt.plot(t,v)
plt.legend(['distance/time','velocity/time'])
plt.show()

Distance travelled at time t = 0s : 0.0
Distance travelled at time t = 10s : 3.8382892720219486
Distance travelled at time t = 100s : 4.0

image.png

In [24]:
import numpy as np 
A = np.array([[1,1,0,1],[0,0,0,1],[1,1,0,0]])
At = np.transpose(A)
print('A*At: ',A.dot(At))
s,v,d = np.linalg.svd(A)
print("S: ",s)
print("V: ",v)
print("D: ",d)

A*At:  [[3 1 2]
 [1 1 0]
 [2 0 2]]
S:  [[ 0.78867513  0.21132487  0.57735027]
 [ 0.21132487  0.78867513 -0.57735027]
 [ 0.57735027 -0.57735027 -0.57735027]]
V:  [2.17532775e+00 1.12603250e+00 5.73316705e-17]
D:  [[ 6.27963030e-01  6.27963030e-01  0.00000000e+00  4.59700843e-01]
 [-3.25057584e-01 -3.25057584e-01  0.00000000e+00  8.88073834e-01]
 [ 7.07106781e-01 -7.07106781e-01  0.00000000e+00 -2.77555756e-16]
 [ 0.00000000e+00  0.00000000e+00  1.00000000e+00  0.00000000e+00]]
In [25]:
"""
A capacitor in an RC circuit with R = 5 KΩ and C = 1 µF is excited with a 2sin(200t) voltage
Write a program to plot the current response of the circuit."""
import numpy as np 
from scipy.integrate import odeint
import matplotlib.pyplot as plt
"""
dI/dt = dV/dt - (I/RC)
"""
def model(y,t):
    R = 5000
    C = 10e-6
    return 400*np.cos(200*t) - y/(R*C)
i0 = 0

t = np.linspace(0,1,100)
sol = odeint(model, i0,t)
plt.plot(t,sol[:,0])
plt.show()

image.png

In [26]:
import matplotlib.pyplot as plt
import numpy as np 
x = np.linspace(0,100,100)
L = 20
f1 = []
f2 = []
f3 = []
for i in x: 
    temp = 0
    for j in range(1,2,2):
        temp = temp + ((-1)**((j-1)/2)/(j**2))*np.sin((j*np.pi*i)/L)
    f1.append(temp* (8/np.pi))
    temp = 0
    for j in range(1,4,2):
        temp = temp + ((-1)**((j-1)/2)/(j**2))*np.sin((j*np.pi*i)/L)
    f2.append(temp* (8/np.pi))
    temp = 0
    for j in range(1,6,2):
        temp = temp + ((-1)**((j-1)/2)/(j**2))*np.sin((j*np.pi*i)/L)
    f3.append(temp* (8/np.pi))
fig,a = plt.subplots(3,1)
a[0].plot(x,f1)
a[1].plot(x,f2)
a[2].plot(x,f3)
plt.show()

image.png

In [27]:
import matplotlib.pyplot as plt
x0 = 2.38
t = np.linspace(0,15,100)
data = []
temp = x0
for i in t:
    temp = temp + 1 + (1/((1+i)**2))
    data.append(temp)
plt.plot(t,data)
plt.xlabel('time in years')
plt.ylabel('height of tree in m')
plt.show()
In [28]:
"""
Given the equation for damped simple harmonic motion
y′′+2y′+2y=cos(2x), y(0)=0,y′(0)=0.Write a program to solve this."""

import numpy as np 
from scipy.integrate import odeint
import matplotlib.pyplot

def model(y,x):
    y,z = y
    return [z,np.cos(2*x)-2*z-2*y]
y0 = [0,0]

x = np.linspace(0,100,1000)

sol = odeint(model, y0, x)
plt.plot(x,sol[:,0])
plt.show()

image.png

In [29]:
x = 0.25
sum1 = 0
for i in range(100):
    sum1 = sum1 + x**i
print("1/ 1-x for x = 0.25: ",sum1)

1/ 1-x for x = 0.25:  1.3333333333333333
In [30]:
"""
Write a program to plot the Lissajous pattern of a sine wave and its derivative"""
import matplotlib.pyplot as plt
import numpy as np 
x = np.linspace(0,2,1000)
d = float(input('enter phase difference: '))
X = []
Y = []
for i in x:
    X.append(np.sin(i*np.pi))
    Y.append(np.sin(i*np.pi + d*np.pi/180))
plt.plot(X,Y)
plt.show()

image.png

In [31]:
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(0,4,1000)
y = []
for i in x:
    y.append(abs(np.sin(np.pi*i)))
plt.plot(x,y)
plt.show()

image.png

In [32]:
import numpy as np 
import matplotlib.pyplot as plt
x = [22,87,5,43,56,73,55,54,11,0,51,5,79,31,27]
print('mean: ', np.mean(x))
print('25th percentile: ',np.percentile(x,25))
plt.hist(x,bins=(50))
plt.show()

mean:  39.93333333333333
25th percentile:  16.5
In [33]:
"""
Implement the function given below and plot its two cycles. Plot its histogram also.
f(t) = sin(πt) + sin(3πt)"""
import numpy as np 
import matplotlib.pyplot as plt 
x = np.linspace(0,10,1000)
f = []
for i in x:
    f.append(np.sin(np.pi*i) + np.sin(3*np.pi*i))
plt.plot(x,f)
plt.show()

image.png

In [34]:
import matplotlib.pyplot as plt
import numpy as np 
from scipy.integrate import odeint

def model(y,t):
    b = 0.05
    m = 2
    L = 1
    g = 9.8
    y,z = y
    dydx = [z,(-b/m)*z + -(g/L)*np.sin(y)]
    return dydx
t = np.linspace(0,5,100)
sol = odeint(model, [0,3], t)
plt.plot(t,sol[:,0])
plt.show()

image.png

In [35]:
import numpy as np 
import matplotlib.pyplot as plt
t = np.linspace(0,20,10000)
f = []
for i in t:
    temp = 0
    for j in range(2,201,2):
        temp = temp + (1/j)*np.sin(j*np.pi*i/20)
    temp *= 4/np.pi
    f.append(1+temp)
plt.plot(t,f)
plt.show()
In [36]:
"""
Implement the functions given below and plot at least two cycles of them. Plot scatter
plot to study their relationship.
f1(t) = cos3πt
f2(t) = cos5πt
"""
import matplotlib.pyplot as plt
import numpy as np 
t = np.linspace(0,2,100)
f1 = np.cos(3*np.pi*t)
f2 = np.cos(5*np.pi*t)
fig,a = plt.subplots(3,1)
a[0].plot(t,f1)
a[1].plot(t,f2)
a[2].scatter(t,f1)
a[2].scatter(t,f2)
plt.show()
In [37]:
"""Write a program to plot the Lissajous pattern of two sine waves of different frequencies."""
import matplotlib.pyplot as plt
import numpy as np 
x = np.linspace(0,2,1000)
a = float(input("input a:"))
b = float(input("input b:"))
d = float(input('enter phase difference: '))
X = []
Y = []
for i in t:
    X.append(np.sin(a*i*np.pi))
    Y.append(np.sin(b*i*np.pi + d*np.pi/180))
plt.plot(X,Y)
plt.show()

image.png

In [38]:
import matplotlib.pyplot as plt
import numpy as np 
x=np.arange(0,40,0.4)
y=[]
big=0
for i in x:
    if i%10==0:
        y.append(0)
        big = i
    else:
        y.append(i/2 - big/2)
plt.plot(x,y)
plt.show()
In [39]:
"""Realize the function y=2+sin(t/2) and plot its 3 complete cycles. Write values of the function
as a csv file such that the sampling time should be the first value followed by its samples."""
import matplotlib.pyplot as plt 
import numpy as np 
import time
tic = time.process_time()
x = np.linspace(0,6*np.pi,100)
y = 2 + np.sin(x/2)
plt.plot(x,y)
plt.show()
x = list(x)
x.insert(0,0)
y = list(y)
data = [x,y]
toc = time.process_time()
data[1].insert(0,(toc-tic)*1000)
# print(data)
np.savetxt("function_sin.csv",data,delimiter = ',')
# this process have done to have equal length of arrays inside data so the csv file would have
# two columns of equal length and in this case, the first row would contain 0, sampling_time_value
# can't enter string so instead of 'sampling time' i put 0
In [40]:
"""Starting from rest, a particle moving in a straight line has an acceleration of a = (2t - 6) m/s2
,
where t is in seconds. Write a program to the particle’s velocity and position. Find the
velocity when t = 6 s, and what is its position when t = 11 s?"""
import numpy as np 
import sympy as sym
t = sym.Symbol('t')
a = 2*t - 6
v = a.integrate(t)
d = v.integrate(t)
print("Velocity: ",v)
print("Distance: ",d)
v6 = v.subs(t,6)
print("Velocity at 6s: ",v6)
d11 = d.subs(t,11)
print("Position at 11s: ",d11)

Velocity:  t**2 - 6*t
Distance:  t**3/3 - 3*t**2
Velocity at 6s:  0
Position at 11s:  242/3
In [42]:
"""Plot a sinc function from time t = 0 to 7. Plot its box plot also and write down the
mean value and first quartile value."""
import numpy as np 
import matplotlib.pyplot as plt
x = np.linspace(0,7,100)
y = np.sinc(x*np.pi/180)
print("Mean: ",np.mean(y))
print("First quartile (25): ",np.percentile(y,25))
plt.boxplot(y,showmeans=(True))
plt.show()

Mean:  0.991811057140368
First quartile (25):  0.9862457560117849

image.png

In [43]:
import numpy as np 
import matplotlib.pyplot as plt
t = np.linspace(0,2*np.pi,100)
v = [[5]*len(t)]
w = np.pi/10
for i in range(1,3):
    temp = []
    for j in t:
        temp.append((40/(((2*i + 1)*np.pi)**2))*np.cos(w*(2*i + 1)*j))
    v.append(temp)
plt.plot(t,v[0])
plt.plot(t,v[1])
plt.plot(t,v[2])
plt.legend(['first term','second term','third term','sum of the terms'])
plt.plot(t,np.add(np.add(v[0],v[1]),v[2]))
plt.show()
In [44]:
"""
f(t) = t ,for t= -5 to 5
= 10-t ,for t=5 to 15
= 0 , otherwise
Plot f(t) forthe vectort = *−5, 15+."""
import numpy as np 
import matplotlib.pyplot as plt
t = np.linspace(-20,20,100)
y = []
for i in t:
    if i>= -5 and i<5:
        y.append(i)
    elif i>=5 and i<15:
        y.append(10-i)
    else:
        y.append(0)
plt.plot(t,y)
plt.show()
In [45]:
"""
A souvenir shop sells Hat, T shirt and Jackets. 3 hats, 2 T shirts and 1 jacket cost Rs. 140. 2
hats, 2 T shirts and 2 jackets cost Rs. 170. 1 hat, 3 T shirts and 2 jackets cost Rs. 180.
program to find the cost of individual items"""
import numpy as np 
A = [[3,2,1],[2,2,2],[1,3,2]]
B = [140,170,180]
sol = np.linalg.solve(A,B)
print("cost of hat", round(sol[0]))
print("cost of tshirt",round(sol[1]))
print("cost of jacket",round(sol[1]))

cost of hat 15
cost of tshirt 25
cost of jacket 25

image.png

In [46]:
import numpy as np 
#did not know the sign of z in theird equation
A = [[2,-1,1,-2],[2,2,-3,1],[1,1,1,0],[4,-3,2,-3]]
B =[-5,-1,-1,-8]
sol = np.linalg.solve(A,B)
print("Solution:",sol)
A = [[2,-1,1,-2],[2,2,-3,1],[1,1,-1,0],[4,-3,2,-3]]
sol = np.linalg.solve(A,B)
print("Solution:",sol)

Solution: [-0.92307692 -0.23076923  0.15384615  1.76923077]
Solution: [1.11022302e-16 1.00000000e+00 2.00000000e+00 3.00000000e+00]

image.png

In [47]:
import matplotlib.pyplot as plt
import numpy as np 
from scipy.integrate import odeint
"""
half life T = ln 2 /  λ
"""
def model(N,t):
    return -np.log(2)*N/5730
i0 = 1000
t = np.linspace(0,2000, 10000) # years
sol = odeint(model, i0, t)
plt.ylabel('Carbon (g)')
plt.xlabel('Time (years)')
plt.plot(t,sol[:,0])
plt.show()
In [48]:
"""
Implement the function given below and plot its two cycles. Plot its box plot also and
write down the mean and thrid quartile value
f(t) = 3+ cos(3πt)+sin(5πt)"""
import numpy as np 
import matplotlib.pyplot as plt
t = np.linspace(0,3,100)
f = 3 + np.cos(3*np.pi*t) + np.sin(5*np.pi*t)
print("Mean: ",np.mean(f))
print("Third quartile value:",np.quantile(f,0.75)) # we can also use np.percentile() for this but we give 75 instead of 0.75
plt.plot(t,f)
plt.show()

Mean:  3.041220561427445
Third quartile value: 3.829496730050256

image.png

In [49]:
import sympy as sym 
from scipy.integrate import quad
t = sym.Symbol('t')
v = 12 - 3*(t**2)
d = v.integrate(t)
a = v.diff(t) # change in velocity
k = a.diff(t) # change in acceleration 
print("Acceration when t = 4: ",a.subs(t,4))
def model(t):
    return 12 - 3*(t**2)
print("displacement from t = 0 to t = 10",round(quad(model,0,10)[0]))
print("distance from t=0 to t=10",d.subs(t,10)-d.subs(t,0))

Acceration when t = 4:  -24
displacement from t = 0 to t = 10 -880
distance from t=0 to t=10 -880
In [50]:
import matplotlib.pyplot as plt
import numpy as np 
x=np.arange(0,40,0.4)
y=[]
big=0
for i in x:
    if i%10==0:
        y.append(0)
        big = i
    elif i>big and i <big+10 and (big+10)%20==0:
        y.append(0)
    else:
        y.append(i/2 - big/2)
plt.plot(x,y)
plt.show()

image.png

In [51]:
import numpy as np 
import matplotlib.pyplot as plt
from scipy.integrate import odeint
t = np.linspace(0,20,100)
k = float(input('enter constant')) # graph depends on k value
def model(v,t):
    return -k*v
v0 = 10
sol = odeint(model,v0,t)
plt.plot(t,sol)
plt.show()

image.png

In [52]:
"""For cooling, rhs is always negative, refer https://web.math.ucsb.edu/~myoshi/cooling.pdf"""

import matplotlib.pyplot as plt
import numpy as np 
from scipy.integrate import odeint

def model(T,t):
    k= -0.1
    Ts = 27
    return k*(T-Ts)
t = np.arange(0,10,1)
t0 = 52
sol = odeint(model, t0, t)
plt.plot(t,sol)
plt.show()

image.png

In [53]:
import numpy as np 
A = np.array([[1,3,5],[1,1,0],[1,1,2],[1,3,3]])
s,v,d = np.linalg.svd(A)
print("S,V,D are",s,v,d,sep='\n')
At = A.transpose()
print("AAt: ",A.dot(At))

S,V,D are
[[-7.63546975e-01 -4.08248290e-01  1.81479992e-02 -5.00000000e-01]
 [-1.02727662e-01  8.16496581e-01  2.69778355e-01 -5.00000000e-01]
 [-3.08182987e-01 -1.38777878e-16  8.09335064e-01  5.00000000e-01]
 [-5.58091650e-01  4.08248290e-01 -5.21408710e-01  5.00000000e-01]]
[7.71115035 1.41421356 0.73359408]
[[-0.22468104 -0.56746741 -0.79214845]
 [ 0.57735027  0.57735027 -0.57735027]
 [ 0.78497458 -0.58706678  0.1979078 ]]
AAt:  [[35  4 14 25]
 [ 4  2  2  4]
 [14  2  6 10]
 [25  4 10 19]]

image.png

In [54]:
import numpy as np 
import matplotlib.pyplot as plt 
t = np.linspace(0,100,10000)
f = (100-t)*np.sin(t)
plt.plot(t,f)
plt.show()

image.png

In [55]:
import matplotlib.pyplot as plt
import numpy as np 
x=np.arange(1,40)
y=[]
big=0
for i in x:
    if i%10==0:
        y.append(-1)
        big = i
    elif i>big and i <big+10 and (big+10)%20==0:
        y.append(-1)
    else:
        y.append(1)
plt.plot(x,y)
plt.show()

image.png

In [56]:
import numpy as np 
def function():
    z = int(input('enter number of equations'))
    print("enter {} numbers".format(z*z))
    entries=list(map(int,input('input numbers with space in between: ').split()))
    if len(entries) == z*z:
        matrix = np.array(entries).reshape(z,z)
        print("Equation matrix:",matrix)
        temp = list(map(int,input('Enter numbers with space in middle: ').split()))
        if len(temp) ==z:
            B =  np.array(temp)
            print("Coefficient matrix: ",B)
        else:
            print("Entered, wrong number of elements")
            print("Try again")
            function()
    else:
        print("Can't reshape as rows*columns does not match total input")
        print("Try again")
        function()
    det = np.linalg.det(matrix)
    if det != 0 :
        sol = np.linalg.solve(matrix,B)
        for i in range(z):
            print("Solution in the order of variables entered:  ",sol[i])
    else:
        print("Determinant is 0, try again")
    
function()

enter 9 numbers

Equation matrix: [[1 2 3]
 [4 5 6]
 [5 4 3]]

Coefficient matrix:  [20 50 30]
Solution in the order of variables entered:   -7505999378950830.0
Solution in the order of variables entered:   1.5011998757901664e+16
Solution in the order of variables entered:   -7505999378950824.0
In [57]:
"""Write a program to implement a simple calculator."""

def calculate():
    operation = input('''
Please type in the math operation you would like to complete:\n
+ for addition\n
- for subtraction\n
* for multiplication\n
/ for division\n
% for modulo \n
// for integer division
''')

    x = int(input('Please enter the first number: '))
    y = int(input('Please enter the second number: '))

    if operation == '+':
        print('{} + {} = '.format(x, y))
        print(x + y)

    elif operation == '-':
        print('{} - {} = '.format(x, y))
        print(x - y)

    elif operation == '*':
        print('{} * {} = '.format(x, y))
        print(x * y)

    elif operation == '/':
        print('{} / {} = '.format(x, y))
        print(x / y)
    elif operation == '%':
        print('{} % {} = '.format(x, y))
        print(x % y)
    elif operation == '//':
        print('{} // {} = '.format(x, y))
        print(x // y)

    else:
        print('You have not typed a valid operator, please run the program again.')

# Call calculate() outside of the function
calculate()

3 / 2 = 
1.5

image.png

In [58]:
x = 0.25
sum1 = 1
for i in range(1,100):
    sum1 = sum1 + x**i
print("result =",sum1)
lhs = 1/(1-x)
rhs = sum1
if lhs == rhs:
    print("LHS = RHS")
else:
    print("lhs != RHS")

result = 1.3333333333333333
LHS = RHS
In [59]:
""".Write a program to find the Harmonic Series up to N terms and Sum of those N terms. Read a
and N through Key board."""
a = int(input('Enter A: '))
d = int(input('Enter D:'))
n = int(input('Enter number of terms: '))
data = []
for i in range(n):
    print("Term {}: ".format(i+1),1/(a+(i*d)))
    data.append(1/(a+(i*d)))
print("sum of terms: ", sum(data))

Term 1:  0.5
Term 2:  0.25
Term 3:  0.16666666666666666
Term 4:  0.125
Term 5:  0.1
Term 6:  0.08333333333333333
Term 7:  0.07142857142857142
Term 8:  0.0625
Term 9:  0.05555555555555555
Term 10:  0.05
sum of terms:  1.4644841269841269

image.png

In [60]:
import numpy as np 
Is =1.17e-9 # reverse saturation current
Vd = 0.4 # voltage across diode, applied in forward bias
Vt = 25.2e-3 #thermal voltae
n = 1 #assuming quality factor to be 1
Id = Is*(np.exp(Vd/(n*Vt))-1)
print("Forward bias current: ",Id)

Forward bias current:  0.009156911378647114

image.png

In [ ]:

image.png

In [61]:
import numpy as np 
data = {'Captain Marvel': 'Apple', 'Thor':'Sun', 'Hulk':'Pot','Doctor Strange': 'Van'}
vote = np.array(['Pot', 'Van', 'Pot', 'Sun', 'Apple', 'Sun', 'Apple', 'Van', 'Van', 'Apple', 'Pot', 'Sun', 'Apple', 'Van', 'Apple',
'Apple'])
for i in data:
    print("Candidate: ",data[i])
print("Votes are ",vote)
results = {}
for i in vote:
    if i in vote and i not in results:
        keyd = [j for j in data if data[j]==i]
        results[keyd[0]] = sum(np.char.count(vote,i))
print(results)

Candidate:  Apple
Candidate:  Sun
Candidate:  Pot
Candidate:  Van
Votes are  ['Pot' 'Van' 'Pot' 'Sun' 'Apple' 'Sun' 'Apple' 'Van' 'Van' 'Apple' 'Pot'
 'Sun' 'Apple' 'Van' 'Apple' 'Apple']
{'Hulk': 3, 'Doctor Strange': 4, 'Thor': 3, 'Captain Marvel': 6}

Square wave image.png

In [62]:
'''Generate the following signals : square wave, ramp, unit step, impulse'''
import numpy as np 
import matplotlib.pyplot as plt
f = 1000
w = 2*np.pi*f
t = np.linspace(0,4*np.pi,100)
sq1 = []
n = 100
'''square wave'''
temp = 0
#assuming a 100 terms
for j in range(n):
    temp = temp + ((1/(2*j + 1))*np.sin((2*j + 1)*w*t))
sq1.append((4/np.pi)*temp)
plt.plot(t,sq1[0])
plt.title("Square waves")
plt.show()

'''ramp signal'''
rs2 = n * t/10
plt.plot(t,rs2)
plt.title('ramp signal')
plt.show()

'''unit step'''
us1 = [0]
for i in range(1,len(t)):
    us1.append(n/100)
plt.plot(t,us1)
plt.title('unit step signal')
plt.show()

'''impulse function'''
us1 = [n/100]
for i in range(1,len(t)):
    us1.append(0)
plt.plot(t,us1)
plt.title('unit impulse signal')
plt.show()

image.png

In [63]:
import numpy as np 
import matplotlib.pyplot as plt
from scipy.integrate import odeint

def model(p,t):
    return 0.1823*p
p0 = 200000
t = np.linspace(0,40,100)
sol = odeint(model, p0,t)
plt.plot(t+2000,sol)
plt.show()
In [64]:
"""Write a program to find the area and perimeter of triangle/ rhombus / square, trapezium."""
def triangle(s1,s2,s3):
    s = (s1+s2+s3)*0.5
    return [(s*(s-s1)*(s-s2)*(s-s3))**0.5, s*2]
def rhombus(d1,d2):
    return [d1*d2*0.5, 2*((d1**2 + d2**2)**0.5)]
def square(s):
    return [s*s, 4*s]
def trapezium(a,b,c,d,h):
    return [(a+b)*h/2, a+b+c+d]
In [65]:
'''Write a program to interchange the row and columns of a matrix f the no. of rows and
column are equal.'''
x=int(input('enter number of rows for matrix: '))
y=int(input('enter number of columns for matrix: '))
entries=list(map(int,input('input number with space in between: ').split()))
if len(entries) == x*y:
    matrix = np.array(entries).reshape(x,y)
matrix_t = np.zeros((y,x))
for i in range(y):
    for j in range(x):
        matrix_t[i][j] = matrix[j][i]
print('old matrix: ',matrix)
print('new matrix: ',matrix_t)

old matrix:  [[1 2 3]
 [4 5 6]
 [7 8 9]]
new matrix:  [[1. 4. 7.]
 [2. 5. 8.]
 [3. 6. 9.]]
In [66]:
'''A second hand car dealer needs the information regarding car in the form of a python
dictionary. The information should include Name of Car, Registration No. ,Colour, .Create
or at least five different cars. After creating the dictionary, delete one row, (not the first
and last) add the following in an that row .
Benz-S Class, KL 37S4321, 2015, 30,000 KM Black'''

data = [
    {'name':'lambo  ','regn no':'KL 47 BT 0000','year':2011,'kilometers':10000,'color':'black'},
    {'name':'ferrari','regn no':'KL 47 BT 1111','year':2012,'kilometers':10000,'color':'black'},
    {'name':'pagani ','regn no':'KL 47 BT 2222','year':2013,'kilometers':10000,'color':'black'},
    {'name':'bugatti','regn no':'KL 47 BT 3333','year':2014,'kilometers':10000,'color':'black'},
    {'name':'hyundai','regn no':'KL 47 BT 4444','year':2015,'kilometers':10000,'color':'black'},]
print(data)
for i in data:
    if data.index(i) != len(data) -1 or data.index(i)!=0:
        data[data.index(i)]['name'] = 'Benz-S Class'
        data[data.index(i)]['regn no'] = 'KL 37S432'
        data[data.index(i)]['year'] = 2015
        data[data.index(i)]['kilometers'] = 30000
        data[data.index(i)]['color'] = 'Black'
print(data)



 
 

[{'name': 'lambo  ', 'regn no': 'KL 47 BT 0000', 'year': 2011, 'kilometers': 10000, 'color': 'black'}, {'name': 'ferrari', 'regn no': 'KL 47 BT 1111', 'year': 2012, 'kilometers': 10000, 'color': 'black'}, {'name': 'pagani ', 'regn no': 'KL 47 BT 2222', 'year': 2013, 'kilometers': 10000, 'color': 'black'}, {'name': 'bugatti', 'regn no': 'KL 47 BT 3333', 'year': 2014, 'kilometers': 10000, 'color': 'black'}, {'name': 'hyundai', 'regn no': 'KL 47 BT 4444', 'year': 2015, 'kilometers': 10000, 'color': 'black'}]
[{'name': 'Benz-S Class', 'regn no': 'KL 37S432', 'year': 2015, 'kilometers': 30000, 'color': 'Black'}, {'name': 'Benz-S Class', 'regn no': 'KL 37S432', 'year': 2015, 'kilometers': 30000, 'color': 'Black'}, {'name': 'Benz-S Class', 'regn no': 'KL 37S432', 'year': 2015, 'kilometers': 30000, 'color': 'Black'}, {'name': 'Benz-S Class', 'regn no': 'KL 37S432', 'year': 2015, 'kilometers': 30000, 'color': 'Black'}, {'name': 'Benz-S Class', 'regn no': 'KL 37S432', 'year': 2015, 'kilometers': 30000, 'color': 'Black'}]